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This is a Experimental Study study.

October 2, 2025Open Access

Computing the Stable Reduction of Hyperelliptic Curves in Residue Characteristic 2

Key Points

The study demonstrates general properties of stable reduction for hyperelliptic curves of genus g.
Researchers worked through explicit examples for hyperelliptic curves up to genus 30, enhancing understanding.
Algorithm refinements improve the computation of stable reductions in residue characteristic 2.
Valuation techniques are utilized to analyze marked curves with their Weierstrass points across varying genus levels.

Abstract

Consider a hyperelliptic curve of genus g over a field K of characteristic zero. After extending K we can view it as a marked curve with its 2g+2 Weierstrass points. We prove some general properties of the stable reduction of this marked curve for a valuation of residue characteristic 2 and refine an existing algorithm for its computation. We work out explicit examples up to genus g=30.

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Cite This Study

Tim Gehrunger (Tue,) studied this question.

synapsesocial.com/papers/68de84bf5b556a9128e1bf48 https://doi.org/https://doi.org/10.48550/arxiv.2506.19663

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